LMFDB - Embedded newform 121.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(1,121)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("121.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.13923111069$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} -1.32051 q^{6} -28.2487 q^{7} -24.4641 q^{8} -26.7128 q^{9} +O(q^{10})$	\(q+2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} -1.32051 q^{6} -28.2487 q^{7} -24.4641 q^{8} -26.7128 q^{9} -3.78461 q^{10} +1.03332 q^{12} +68.4641 q^{13} -69.6077 q^{14} +0.823085 q^{15} -44.8564 q^{16} +55.3538 q^{17} -65.8231 q^{18} -55.1769 q^{19} +2.96152 q^{20} +15.1384 q^{21} -178.315 q^{23} +13.1103 q^{24} -122.641 q^{25} +168.703 q^{26} +28.7846 q^{27} +54.4693 q^{28} +113.172 q^{29} +2.02817 q^{30} +70.8128 q^{31} +85.1821 q^{32} +136.397 q^{34} +43.3872 q^{35} +51.5077 q^{36} -210.664 q^{37} -135.962 q^{38} -36.6898 q^{39} +37.5744 q^{40} +191.928 q^{41} +37.3027 q^{42} -208.210 q^{43} +41.0282 q^{45} -439.387 q^{46} +512.515 q^{47} +24.0385 q^{48} +454.990 q^{49} -302.200 q^{50} -29.6640 q^{51} -132.013 q^{52} -375.449 q^{53} +70.9282 q^{54} +691.079 q^{56} +29.5692 q^{57} +278.867 q^{58} -506.508 q^{59} -1.58708 q^{60} -468.697 q^{61} +174.490 q^{62} +754.603 q^{63} +568.749 q^{64} -105.154 q^{65} -289.895 q^{67} -106.733 q^{68} +95.5589 q^{69} +106.910 q^{70} -394.010 q^{71} +653.505 q^{72} +289.538 q^{73} -519.098 q^{74} +65.7231 q^{75} +106.392 q^{76} -90.4074 q^{78} -169.587 q^{79} +68.8949 q^{80} +705.820 q^{81} +472.931 q^{82} -303.331 q^{83} -29.1900 q^{84} -85.0179 q^{85} -513.051 q^{86} -60.6486 q^{87} -1146.68 q^{89} +101.098 q^{90} -1934.02 q^{91} +343.828 q^{92} -37.9485 q^{93} +1262.89 q^{94} +84.7461 q^{95} -45.6489 q^{96} +641.600 q^{97} +1121.14 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} + 2 q^{9} + 34 q^{10} - 88 q^{12} + 130 q^{13} - 160 q^{14} + 64 q^{15} - 62 q^{16} - 14 q^{17} - 194 q^{18} - 48 q^{19} - 98 q^{20} - 136 q^{21} - 128 q^{23} + 144 q^{24} - 176 q^{25} - 106 q^{26} + 16 q^{27} + 296 q^{28} - 30 q^{29} - 280 q^{30} - 184 q^{31} + 302 q^{32} + 446 q^{34} - 128 q^{35} + 394 q^{36} + 126 q^{37} - 168 q^{38} - 496 q^{39} + 186 q^{40} + 370 q^{41} + 712 q^{42} - 264 q^{43} - 202 q^{45} - 664 q^{46} + 256 q^{47} + 152 q^{48} + 522 q^{49} - 64 q^{50} + 488 q^{51} + 602 q^{52} - 162 q^{53} + 128 q^{54} + 336 q^{56} - 24 q^{57} + 918 q^{58} - 1304 q^{59} + 752 q^{60} - 300 q^{61} + 1312 q^{62} + 1336 q^{63} - 262 q^{64} - 626 q^{65} - 656 q^{67} - 934 q^{68} - 280 q^{69} + 872 q^{70} - 1176 q^{71} + 150 q^{72} - 668 q^{73} - 2022 q^{74} + 464 q^{75} + 192 q^{76} + 1960 q^{78} + 416 q^{79} + 214 q^{80} + 26 q^{81} - 322 q^{82} - 960 q^{83} - 1832 q^{84} + 502 q^{85} - 264 q^{86} + 1008 q^{87} - 1074 q^{89} + 1186 q^{90} - 688 q^{91} + 944 q^{92} + 1864 q^{93} + 2408 q^{94} + 24 q^{95} - 1664 q^{96} - 338 q^{97} + 822 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 + 2 * q^9 + 34 * q^10 - 88 * q^12 + 130 * q^13 - 160 * q^14 + 64 * q^15 - 62 * q^16 - 14 * q^17 - 194 * q^18 - 48 * q^19 - 98 * q^20 - 136 * q^21 - 128 * q^23 + 144 * q^24 - 176 * q^25 - 106 * q^26 + 16 * q^27 + 296 * q^28 - 30 * q^29 - 280 * q^30 - 184 * q^31 + 302 * q^32 + 446 * q^34 - 128 * q^35 + 394 * q^36 + 126 * q^37 - 168 * q^38 - 496 * q^39 + 186 * q^40 + 370 * q^41 + 712 * q^42 - 264 * q^43 - 202 * q^45 - 664 * q^46 + 256 * q^47 + 152 * q^48 + 522 * q^49 - 64 * q^50 + 488 * q^51 + 602 * q^52 - 162 * q^53 + 128 * q^54 + 336 * q^56 - 24 * q^57 + 918 * q^58 - 1304 * q^59 + 752 * q^60 - 300 * q^61 + 1312 * q^62 + 1336 * q^63 - 262 * q^64 - 626 * q^65 - 656 * q^67 - 934 * q^68 - 280 * q^69 + 872 * q^70 - 1176 * q^71 + 150 * q^72 - 668 * q^73 - 2022 * q^74 + 464 * q^75 + 192 * q^76 + 1960 * q^78 + 416 * q^79 + 214 * q^80 + 26 * q^81 - 322 * q^82 - 960 * q^83 - 1832 * q^84 + 502 * q^85 - 264 * q^86 + 1008 * q^87 - 1074 * q^89 + 1186 * q^90 - 688 * q^91 + 944 * q^92 + 1864 * q^93 + 2408 * q^94 + 24 * q^95 - 1664 * q^96 - 338 * q^97 + 822 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.46410	0.871191	0.435596	−	0.900142i	$-0.356538\pi$
$2$	2.46410	0.871191	0.435596	+	0.900142i	$0.356538\pi$
$3$	−0.535898	−0.103134	−0.0515668	−	0.998670i	$-0.516422\pi$
$3$	−0.535898	−0.103134	−0.0515668	+	0.998670i	$0.516422\pi$
$4$	−1.92820	−0.241025
$5$	−1.53590	−0.137375	−0.0686875	−	0.997638i	$-0.521881\pi$
$5$	−1.53590	−0.137375	−0.0686875	+	0.997638i	$0.521881\pi$
$6$	−1.32051	−0.0898492
$7$	−28.2487	−1.52529	−0.762644	−	0.646819i	$-0.776099\pi$
$7$	−28.2487	−1.52529	−0.762644	+	0.646819i	$0.776099\pi$
$8$	−24.4641	−1.08117
$9$	−26.7128	−0.989363
$10$	−3.78461	−0.119680
$11$	0	0
$11$	0	0
$12$	1.03332	0.0248578
$13$	68.4641	1.46066	0.730328	−	0.683097i	$-0.239367\pi$
$13$	68.4641	1.46066	0.730328	+	0.683097i	$0.239367\pi$
$14$	−69.6077	−1.32882
$15$	0.823085	0.0141680
$16$	−44.8564	−0.700881
$17$	55.3538	0.789722	0.394861	−	0.918741i	$-0.370793\pi$
$17$	55.3538	0.789722	0.394861	+	0.918741i	$0.370793\pi$
$18$	−65.8231	−0.861925
$19$	−55.1769	−0.666234	−0.333117	−	0.942885i	$-0.608100\pi$
$19$	−55.1769	−0.666234	−0.333117	+	0.942885i	$0.608100\pi$
$20$	2.96152	0.0331108
$21$	15.1384	0.157308
$22$	0	0
$23$	−178.315	−1.61658	−0.808290	−	0.588785i	$-0.799606\pi$
$23$	−178.315	−1.61658	−0.808290	+	0.588785i	$0.799606\pi$
$24$	13.1103	0.111505
$25$	−122.641	−0.981128
$26$	168.703	1.27251
$27$	28.7846	0.205170
$28$	54.4693	0.367633
$29$	113.172	0.724671	0.362336	−	0.932048i	$-0.381979\pi$
$29$	113.172	0.724671	0.362336	+	0.932048i	$0.381979\pi$
$30$	2.02817	0.0123430
$31$	70.8128	0.410269	0.205135	−	0.978734i	$-0.434237\pi$
$31$	70.8128	0.410269	0.205135	+	0.978734i	$0.434237\pi$
$32$	85.1821	0.470569
$33$	0	0
$34$	136.397	0.687999
$35$	43.3872	0.209536
$36$	51.5077	0.238462
$37$	−210.664	−0.936026	−0.468013	−	0.883722i	$-0.655030\pi$
$37$	−210.664	−0.936026	−0.468013	+	0.883722i	$0.655030\pi$
$38$	−135.962	−0.580418
$39$	−36.6898	−0.150643
$40$	37.5744	0.148526
$41$	191.928	0.731077	0.365538	−	0.930796i	$-0.380885\pi$
$41$	191.928	0.731077	0.365538	+	0.930796i	$0.380885\pi$
$42$	37.3027	0.137046
$43$	−208.210	−0.738413	−0.369207	−	0.929347i	$-0.620371\pi$
$43$	−208.210	−0.738413	−0.369207	+	0.929347i	$0.620371\pi$
$44$	0	0
$45$	41.0282	0.135914
$46$	−439.387	−1.40835
$47$	512.515	1.59060	0.795298	−	0.606218i	$-0.207314\pi$
$47$	512.515	1.59060	0.795298	+	0.606218i	$0.207314\pi$
$48$	24.0385	0.0722845
$49$	454.990	1.32650
$50$	−302.200	−0.854750
$51$	−29.6640	−0.0814470
$52$	−132.013	−0.352055
$53$	−375.449	−0.973054	−0.486527	−	0.873666i	$-0.661736\pi$
$53$	−375.449	−0.973054	−0.486527	+	0.873666i	$0.661736\pi$
$54$	70.9282	0.178743
$55$	0	0
$56$	691.079	1.64910
$57$	29.5692	0.0687112
$58$	278.867	0.631327
$59$	−506.508	−1.11766	−0.558828	−	0.829284i	$-0.688749\pi$
$59$	−506.508	−1.11766	−0.558828	+	0.829284i	$0.688749\pi$
$60$	−1.58708	−0.00341484
$61$	−468.697	−0.983779	−0.491890	−	0.870658i	$-0.663694\pi$
$61$	−468.697	−0.983779	−0.491890	+	0.870658i	$0.663694\pi$
$62$	174.490	0.357423
$63$	754.603	1.50906
$64$	568.749	1.11084
$65$	−105.154	−0.200657
$66$	0	0
$67$	−289.895	−0.528601	−0.264301	−	0.964440i	$-0.585141\pi$
$67$	−289.895	−0.528601	−0.264301	+	0.964440i	$0.585141\pi$
$68$	−106.733	−0.190343
$69$	95.5589	0.166724
$70$	106.910	0.182546
$71$	−394.010	−0.658597	−0.329299	−	0.944226i	$-0.606812\pi$
$71$	−394.010	−0.658597	−0.329299	+	0.944226i	$0.606812\pi$
$72$	653.505	1.06967
$73$	289.538	0.464218	0.232109	−	0.972690i	$-0.425437\pi$
$73$	289.538	0.464218	0.232109	+	0.972690i	$0.425437\pi$
$74$	−519.098	−0.815458
$75$	65.7231	0.101187
$76$	106.392	0.160579
$77$	0	0
$78$	−90.4074	−0.131239
$79$	−169.587	−0.241519	−0.120760	−	0.992682i	$-0.538533\pi$
$79$	−169.587	−0.241519	−0.120760	+	0.992682i	$0.538533\pi$
$80$	68.8949	0.0962835
$81$	705.820	0.968203
$82$	472.931	0.636908
$83$	−303.331	−0.401143	−0.200572	−	0.979679i	$-0.564280\pi$
$83$	−303.331	−0.401143	−0.200572	+	0.979679i	$0.564280\pi$
$84$	−29.1900	−0.0379153
$85$	−85.0179	−0.108488
$86$	−513.051	−0.643299
$87$	−60.6486	−0.0747380
$88$	0	0
$89$	−1146.68	−1.36571	−0.682854	−	0.730555i	$-0.739262\pi$
$89$	−1146.68	−1.36571	−0.682854	+	0.730555i	$0.739262\pi$
$90$	101.098	0.118407
$91$	−1934.02	−2.22792
$92$	343.828	0.389637
$93$	−37.9485	−0.0423126
$94$	1262.89	1.38571
$95$	84.7461	0.0915239
$96$	−45.6489	−0.0485315
$97$	641.600	0.671594	0.335797	−	0.941934i	$-0.390994\pi$
$97$	641.600	0.671594	0.335797	+	0.941934i	$0.390994\pi$
$98$	1121.14	1.15564
$99$	0	0
$100$	236.477	0.236477
$101$	1107.57	1.09116	0.545580	−	0.838058i	$-0.316309\pi$
$101$	1107.57	1.09116	0.545580	+	0.838058i	$0.316309\pi$
$102$	−73.0952	−0.0709559
$103$	−298.297	−0.285360	−0.142680	−	0.989769i	$-0.545572\pi$
$103$	−298.297	−0.285360	−0.142680	+	0.989769i	$0.545572\pi$
$104$	−1674.91	−1.57922
$105$	−23.2511	−0.0216102
$106$	−925.144	−0.847716
$107$	−598.126	−0.540402	−0.270201	−	0.962804i	$-0.587090\pi$
$107$	−598.126	−0.540402	−0.270201	+	0.962804i	$0.587090\pi$
$108$	−55.5026	−0.0494513
$109$	−1530.16	−1.34461	−0.672305	−	0.740275i	$-0.734695\pi$
$109$	−1530.16	−1.34461	−0.672305	+	0.740275i	$0.734695\pi$
$110$	0	0
$111$	112.895	0.0965358
$112$	1267.14	1.06905
$113$	−151.010	−0.125716	−0.0628578	−	0.998022i	$-0.520021\pi$
$113$	−151.010	−0.125716	−0.0628578	+	0.998022i	$0.520021\pi$
$114$	72.8616	0.0598606
$115$	273.874	0.222077
$116$	−218.218	−0.174664
$117$	−1828.87	−1.44512
$118$	−1248.09	−0.973692
$119$	−1563.67	−1.20455
$120$	−20.1360	−0.0153180
$121$	0	0
$122$	−1154.92	−0.857060
$123$	−102.854	−0.0753987
$124$	−136.541	−0.0988853
$125$	380.351	0.272157
$126$	1859.42	1.31468
$127$	−695.749	−0.486124	−0.243062	−	0.970011i	$-0.578152\pi$
$127$	−695.749	−0.486124	−0.243062	+	0.970011i	$0.578152\pi$
$128$	719.998	0.497183
$129$	111.580	0.0761553
$130$	−259.110	−0.174811
$131$	1665.68	1.11093	0.555463	−	0.831541i	$-0.312541\pi$
$131$	1665.68	1.11093	0.555463	+	0.831541i	$0.312541\pi$
$132$	0	0
$133$	1558.68	1.01620
$134$	−714.330	−0.460513
$135$	−44.2102	−0.0281853
$136$	−1354.18	−0.853824
$137$	−1605.48	−1.00121	−0.500603	−	0.865677i	$-0.666888\pi$
$137$	−1605.48	−1.00121	−0.500603	+	0.865677i	$0.666888\pi$
$138$	235.467	0.145248
$139$	−1069.30	−0.652495	−0.326248	−	0.945284i	$-0.605784\pi$
$139$	−1069.30	−0.652495	−0.326248	+	0.945284i	$0.605784\pi$
$140$	−83.6592	−0.0505035
$141$	−274.656	−0.164044
$142$	−970.881	−0.573765
$143$	0	0
$144$	1198.24	0.693426
$145$	−173.820	−0.0995517
$146$	713.452	0.404423
$147$	−243.828	−0.136807
$148$	406.203	0.225606
$149$	−355.172	−0.195281	−0.0976403	−	0.995222i	$-0.531129\pi$
$149$	−355.172	−0.195281	−0.0976403	+	0.995222i	$0.531129\pi$
$150$	161.948	0.0881536
$151$	1879.55	1.01295	0.506476	−	0.862254i	$-0.330948\pi$
$151$	1879.55	1.01295	0.506476	+	0.862254i	$0.330948\pi$
$152$	1349.85	0.720313
$153$	−1478.66	−0.781322
$154$	0	0
$155$	−108.761	−0.0563607
$156$	70.7454	0.0363087
$157$	2499.99	1.27083	0.635417	−	0.772169i	$-0.280828\pi$
$157$	2499.99	1.27083	0.635417	+	0.772169i	$0.280828\pi$
$158$	−417.880	−0.210410
$159$	201.202	0.100355
$160$	−130.831	−0.0646444
$161$	5037.18	2.46575
$162$	1739.21	0.843491
$163$	1863.02	0.895235	0.447617	−	0.894225i	$-0.352273\pi$
$163$	1863.02	0.895235	0.447617	+	0.894225i	$0.352273\pi$
$164$	−370.077	−0.176208
$165$	0	0
$166$	−747.438	−0.349473
$167$	−2647.27	−1.22666	−0.613328	−	0.789828i	$-0.710170\pi$
$167$	−2647.27	−1.22666	−0.613328	+	0.789828i	$0.710170\pi$
$168$	−370.348	−0.170077
$169$	2490.33	1.13352
$170$	−209.493	−0.0945138
$171$	1473.93	0.659148
$172$	401.472	0.177976
$173$	−2109.38	−0.927015	−0.463507	−	0.886093i	$-0.653409\pi$
$173$	−2109.38	−0.927015	−0.463507	+	0.886093i	$0.653409\pi$
$174$	−149.444	−0.0651111
$175$	3464.45	1.49650
$176$	0	0
$177$	271.437	0.115268
$178$	−2825.54	−1.18979
$179$	1391.25	0.580931	0.290465	−	0.956886i	$-0.406190\pi$
$179$	1391.25	0.580931	0.290465	+	0.956886i	$0.406190\pi$
$180$	−79.1106	−0.0327587
$181$	3701.40	1.52002	0.760008	−	0.649913i	$-0.225195\pi$
$181$	3701.40	1.52002	0.760008	+	0.649913i	$0.225195\pi$
$182$	−4765.63	−1.94094
$183$	251.174	0.101461
$184$	4362.32	1.74780
$185$	323.559	0.128586
$186$	−93.5088	−0.0368624
$187$	0	0
$188$	−988.234	−0.383374
$189$	−813.128	−0.312944
$190$	208.823	0.0797348
$191$	−3533.03	−1.33844	−0.669218	−	0.743066i	$-0.733371\pi$
$191$	−3533.03	−1.33844	−0.669218	+	0.743066i	$0.733371\pi$
$192$	−304.791	−0.114565
$193$	2605.66	0.971811	0.485906	−	0.874011i	$-0.338490\pi$
$193$	2605.66	0.971811	0.485906	+	0.874011i	$0.338490\pi$
$194$	1580.97	0.585087
$195$	56.3518	0.0206945
$196$	−877.313	−0.319720
$197$	−719.202	−0.260107	−0.130053	−	0.991507i	$-0.541515\pi$
$197$	−719.202	−0.260107	−0.130053	+	0.991507i	$0.541515\pi$
$198$	0	0
$199$	1035.15	0.368744	0.184372	−	0.982857i	$-0.440975\pi$
$199$	1035.15	0.368744	0.184372	+	0.982857i	$0.440975\pi$
$200$	3000.30	1.06077
$201$	155.354	0.0545166
$202$	2729.16	0.950610
$203$	−3196.96	−1.10533
$204$	57.1983	0.0196308
$205$	−294.782	−0.100432
$206$	−735.035	−0.248604
$207$	4763.30	1.59938
$208$	−3071.05	−1.02375
$209$	0	0
$210$	−57.2931	−0.0188267
$211$	356.297	0.116249	0.0581244	−	0.998309i	$-0.481488\pi$
$211$	356.297	0.116249	0.0581244	+	0.998309i	$0.481488\pi$
$212$	723.941	0.234531
$213$	211.149	0.0679236
$214$	−1473.84	−0.470793
$215$	319.790	0.101439
$216$	−704.190	−0.221824
$217$	−2000.37	−0.625779
$218$	−3770.46	−1.17141
$219$	−155.163	−0.0478765
$220$	0	0
$221$	3789.75	1.15351
$222$	278.184	0.0841012
$223$	−292.544	−0.0878485	−0.0439242	−	0.999035i	$-0.513986\pi$
$223$	−292.544	−0.0878485	−0.0439242	+	0.999035i	$0.513986\pi$
$224$	−2406.28	−0.717753
$225$	3276.09	0.970692
$226$	−372.105	−0.109522
$227$	−5604.04	−1.63856	−0.819280	−	0.573394i	$-0.805626\pi$
$227$	−5604.04	−1.63856	−0.819280	+	0.573394i	$0.805626\pi$
$228$	−57.0155	−0.0165611
$229$	−5654.38	−1.63167	−0.815833	−	0.578287i	$-0.803721\pi$
$229$	−5654.38	−1.63167	−0.815833	+	0.578287i	$0.803721\pi$
$230$	674.854	0.193472
$231$	0	0
$232$	−2768.65	−0.783493
$233$	2553.08	0.717845	0.358923	−	0.933367i	$-0.383144\pi$
$233$	2553.08	0.717845	0.358923	+	0.933367i	$0.383144\pi$
$234$	−4506.52	−1.25898
$235$	−787.171	−0.218508
$236$	976.650	0.269383
$237$	90.8814	0.0249088
$238$	−3853.05	−1.04940
$239$	−5297.27	−1.43369	−0.716845	−	0.697233i	$-0.754414\pi$
$239$	−5297.27	−1.43369	−0.716845	+	0.697233i	$0.754414\pi$
$240$	−36.9207	−0.00993008
$241$	4145.14	1.10793	0.553966	−	0.832539i	$-0.313114\pi$
$241$	4145.14	1.10793	0.553966	+	0.832539i	$0.313114\pi$
$242$	0	0
$243$	−1155.43	−0.305025
$244$	903.744	0.237116
$245$	−698.818	−0.182228
$246$	−253.443	−0.0656867
$247$	−3777.64	−0.973139
$248$	−1732.37	−0.443571
$249$	162.554	0.0413714
$250$	937.225	0.237101
$251$	−1788.13	−0.449665	−0.224832	−	0.974397i	$-0.572183\pi$
$251$	−1788.13	−0.449665	−0.224832	+	0.974397i	$0.572183\pi$
$252$	−1455.03	−0.363723
$253$	0	0
$254$	−1714.40	−0.423507
$255$	45.5609	0.0111888
$256$	−2775.84	−0.677696
$257$	5167.01	1.25412	0.627061	−	0.778970i	$-0.284258\pi$
$257$	5167.01	1.25412	0.627061	+	0.778970i	$0.284258\pi$
$258$	274.943	0.0663458
$259$	5950.99	1.42771
$260$	202.758	0.0483636
$261$	−3023.14	−0.716963
$262$	4104.41	0.967829
$263$	−57.6791	−0.0135234	−0.00676169	−	0.999977i	$-0.502152\pi$
$263$	−57.6791	−0.0135234	−0.00676169	+	0.999977i	$0.502152\pi$
$264$	0	0
$265$	576.651	0.133673
$266$	3840.74	0.885304
$267$	614.505	0.140851
$268$	558.976	0.127406
$269$	−3028.06	−0.686335	−0.343167	−	0.939274i	$-0.611500\pi$
$269$	−3028.06	−0.686335	−0.343167	+	0.939274i	$0.611500\pi$
$270$	−108.939	−0.0245548
$271$	−1487.84	−0.333504	−0.166752	−	0.985999i	$-0.553328\pi$
$271$	−1487.84	−0.333504	−0.166752	+	0.985999i	$0.553328\pi$
$272$	−2482.97	−0.553501
$273$	1036.44	0.229774
$274$	−3956.06	−0.872241
$275$	0	0
$276$	−184.257	−0.0401847
$277$	7460.46	1.61825	0.809126	−	0.587635i	$-0.199941\pi$
$277$	7460.46	1.61825	0.809126	+	0.587635i	$0.199941\pi$
$278$	−2634.86	−0.568448
$279$	−1891.61	−0.405906
$280$	−1061.43	−0.226544
$281$	900.155	0.191099	0.0955493	−	0.995425i	$-0.469539\pi$
$281$	900.155	0.191099	0.0955493	+	0.995425i	$0.469539\pi$
$282$	−676.781	−0.142914
$283$	6486.92	1.36257	0.681285	−	0.732018i	$-0.261422\pi$
$283$	6486.92	1.36257	0.681285	+	0.732018i	$0.261422\pi$
$284$	759.732	0.158739
$285$	−45.4153	−0.00943920
$286$	0	0
$287$	−5421.72	−1.11510
$288$	−2275.45	−0.465564
$289$	−1848.95	−0.376339
$290$	−428.311	−0.0867286
$291$	−343.832	−0.0692639
$292$	−558.289	−0.111888
$293$	6129.38	1.22212	0.611062	−	0.791583i	$-0.290743\pi$
$293$	6129.38	1.22212	0.611062	+	0.791583i	$0.290743\pi$
$294$	−600.818	−0.119185
$295$	777.944	0.153538
$296$	5153.71	1.01200
$297$	0	0
$298$	−875.179	−0.170127
$299$	−12208.2	−2.36127
$300$	−126.728	−0.0243887
$301$	5881.67	1.12629
$302$	4631.41	0.882476
$303$	−593.545	−0.112535
$304$	2475.04	0.466951
$305$	719.872	0.135147
$306$	−3643.56	−0.680681
$307$	5377.67	0.999740	0.499870	−	0.866101i	$-0.333381\pi$
$307$	5377.67	0.999740	0.499870	+	0.866101i	$0.333381\pi$
$308$	0	0
$309$	159.857	0.0294303
$310$	−267.999	−0.0491010
$311$	−6066.41	−1.10609	−0.553046	−	0.833151i	$-0.686535\pi$
$311$	−6066.41	−1.10609	−0.553046	+	0.833151i	$0.686535\pi$
$312$	897.583	0.162871
$313$	3241.18	0.585311	0.292655	−	0.956218i	$-0.405461\pi$
$313$	3241.18	0.585311	0.292655	+	0.956218i	$0.405461\pi$
$314$	6160.23	1.10714
$315$	−1158.99	−0.207307
$316$	326.998	0.0582123
$317$	6519.32	1.15508	0.577542	−	0.816361i	$-0.304012\pi$
$317$	6519.32	1.15508	0.577542	+	0.816361i	$0.304012\pi$
$318$	495.783	0.0874281
$319$	0	0
$320$	−873.540	−0.152601
$321$	320.535	0.0557336
$322$	12412.1	2.14814
$323$	−3054.25	−0.526140
$324$	−1360.97	−0.233362
$325$	−8396.51	−1.43309
$326$	4590.68	0.779921
$327$	820.008	0.138675
$328$	−4695.35	−0.790419
$329$	−14477.9	−2.42612
$330$	0	0
$331$	5879.55	0.976343	0.488171	−	0.872748i	$-0.337664\pi$
$331$	5879.55	0.976343	0.488171	+	0.872748i	$0.337664\pi$
$332$	584.883	0.0966857
$333$	5627.43	0.926070
$334$	−6523.13	−1.06865
$335$	445.249	0.0726166
$336$	−679.056	−0.110255
$337$	1342.66	0.217031	0.108516	−	0.994095i	$-0.465390\pi$
$337$	1342.66	0.217031	0.108516	+	0.994095i	$0.465390\pi$
$338$	6136.43	0.987509
$339$	80.9262	0.0129655
$340$	163.932	0.0261484
$341$	0	0
$342$	3631.91	0.574244
$343$	−3163.56	−0.498007
$344$	5093.68	0.798351
$345$	−146.769	−0.0229037
$346$	−5197.74	−0.807607
$347$	−5650.03	−0.874091	−0.437046	−	0.899439i	$-0.643975\pi$
$347$	−5650.03	−0.874091	−0.437046	+	0.899439i	$0.643975\pi$
$348$	116.943	0.0180138
$349$	−1249.55	−0.191653	−0.0958266	−	0.995398i	$-0.530549\pi$
$349$	−1249.55	−0.191653	−0.0958266	+	0.995398i	$0.530549\pi$
$350$	8536.76	1.30374
$351$	1970.71	0.299683
$352$	0	0
$353$	5984.25	0.902293	0.451147	−	0.892450i	$-0.351015\pi$
$353$	5984.25	0.902293	0.451147	+	0.892450i	$0.351015\pi$
$354$	668.848	0.100420
$355$	605.160	0.0904748
$356$	2211.04	0.329170
$357$	837.971	0.124230
$358$	3428.17	0.506102
$359$	−2176.01	−0.319904	−0.159952	−	0.987125i	$-0.551134\pi$
$359$	−2176.01	−0.319904	−0.159952	+	0.987125i	$0.551134\pi$
$360$	−1003.72	−0.146946
$361$	−3814.51	−0.556132
$362$	9120.63	1.32423
$363$	0	0
$364$	3729.19	0.536985
$365$	−444.701	−0.0637719
$366$	618.919	0.0883918
$367$	−8464.39	−1.20392	−0.601958	−	0.798528i	$-0.705613\pi$
$367$	−8464.39	−1.20392	−0.601958	+	0.798528i	$0.705613\pi$
$368$	7998.59	1.13303
$369$	−5126.94	−0.723301
$370$	797.281	0.112023
$371$	10605.9	1.48419
$372$	73.1723	0.0101984
$373$	−4248.93	−0.589816	−0.294908	−	0.955526i	$-0.595289\pi$
$373$	−4248.93	−0.589816	−0.294908	+	0.955526i	$0.595289\pi$
$374$	0	0
$375$	−203.830	−0.0280686
$376$	−12538.2	−1.71971
$377$	7748.20	1.05850
$378$	−2003.63	−0.272634
$379$	4852.93	0.657727	0.328863	−	0.944378i	$-0.393334\pi$
$379$	4852.93	0.657727	0.328863	+	0.944378i	$0.393334\pi$
$380$	−163.408	−0.0220596
$381$	372.851	0.0501357
$382$	−8705.75	−1.16603
$383$	−8181.81	−1.09157	−0.545785	−	0.837926i	$-0.683768\pi$
$383$	−8181.81	−1.09157	−0.545785	+	0.837926i	$0.683768\pi$
$384$	−385.846	−0.0512763
$385$	0	0
$386$	6420.61	0.846634
$387$	5561.88	0.730559
$388$	−1237.13	−0.161871
$389$	1254.82	0.163552	0.0817761	−	0.996651i	$-0.473941\pi$
$389$	1254.82	0.163552	0.0817761	+	0.996651i	$0.473941\pi$
$390$	138.857	0.0180289
$391$	−9870.44	−1.27665
$392$	−11130.9	−1.43417
$393$	−892.636	−0.114574
$394$	−1772.19	−0.226603
$395$	260.469	0.0331787
$396$	0	0
$397$	−11519.3	−1.45627	−0.728133	−	0.685436i	$-0.759612\pi$
$397$	−11519.3	−1.45627	−0.728133	+	0.685436i	$0.759612\pi$
$398$	2550.72	0.321247
$399$	−835.292	−0.104804
$400$	5501.24	0.687654
$401$	−1500.66	−0.186882	−0.0934409	−	0.995625i	$-0.529787\pi$
$401$	−1500.66	−0.186882	−0.0934409	+	0.995625i	$0.529787\pi$
$402$	382.809	0.0474944
$403$	4848.13	0.599262
$404$	−2135.62	−0.262998
$405$	−1084.07	−0.133007
$406$	−7877.63	−0.962956
$407$	0	0
$408$	725.704	0.0880581
$409$	91.3936	0.0110492	0.00552460	−	0.999985i	$-0.498241\pi$
$409$	91.3936	0.0110492	0.00552460	+	0.999985i	$0.498241\pi$
$410$	−726.373	−0.0874952
$411$	860.372	0.103258
$412$	575.178	0.0687791
$413$	14308.2	1.70475
$414$	11737.3	1.39337
$415$	465.885	0.0551070
$416$	5831.91	0.687339
$417$	573.036	0.0672942
$418$	0	0
$419$	−1880.83	−0.219295	−0.109648	−	0.993971i	$-0.534972\pi$
$419$	−1880.83	−0.219295	−0.109648	+	0.993971i	$0.534972\pi$
$420$	44.8329	0.00520862
$421$	−7279.83	−0.842748	−0.421374	−	0.906887i	$-0.638452\pi$
$421$	−7279.83	−0.842748	−0.421374	+	0.906887i	$0.638452\pi$
$422$	877.951	0.101275
$423$	−13690.7	−1.57368
$424$	9185.01	1.05204
$425$	−6788.65	−0.774819
$426$	520.294	0.0591745
$427$	13240.1	1.50055
$428$	1153.31	0.130251
$429$	0	0
$430$	787.994	0.0883732
$431$	6870.61	0.767855	0.383928	−	0.923363i	$-0.374571\pi$
$431$	6870.61	0.767855	0.383928	+	0.923363i	$0.374571\pi$
$432$	−1291.17	−0.143800
$433$	1121.32	0.124451	0.0622255	−	0.998062i	$-0.480180\pi$
$433$	1121.32	0.124451	0.0622255	+	0.998062i	$0.480180\pi$
$434$	−4929.11	−0.545173
$435$	93.1500	0.0102671
$436$	2950.45	0.324085
$437$	9838.89	1.07702
$438$	−382.338	−0.0417096
$439$	7114.94	0.773525	0.386763	−	0.922179i	$-0.373593\pi$
$439$	7114.94	0.773525	0.386763	+	0.922179i	$0.373593\pi$
$440$	0	0
$441$	−12154.1	−1.31239
$442$	9338.33	1.00493
$443$	−14057.4	−1.50764	−0.753822	−	0.657079i	$-0.771792\pi$
$443$	−14057.4	−1.50764	−0.753822	+	0.657079i	$0.771792\pi$
$444$	−217.684	−0.0232676
$445$	1761.19	0.187614
$446$	−720.859	−0.0765328
$447$	190.336	0.0201400
$448$	−16066.4	−1.69435
$449$	−15323.9	−1.61064	−0.805320	−	0.592840i	$-0.798007\pi$
$449$	−15323.9	−1.61064	−0.805320	+	0.592840i	$0.798007\pi$
$450$	8072.61	0.845659
$451$	0	0
$452$	291.179	0.0303006
$453$	−1007.25	−0.104470
$454$	−13808.9	−1.42750
$455$	2970.46	0.306060
$456$	−723.384	−0.0742885
$457$	−7212.20	−0.738233	−0.369117	−	0.929383i	$-0.620340\pi$
$457$	−7212.20	−0.738233	−0.369117	+	0.929383i	$0.620340\pi$
$458$	−13933.0	−1.42149
$459$	1593.34	0.162028
$460$	−528.085	−0.0535263
$461$	−10159.6	−1.02642	−0.513212	−	0.858262i	$-0.671544\pi$
$461$	−10159.6	−1.02642	−0.513212	+	0.858262i	$0.671544\pi$
$462$	0	0
$463$	−10292.0	−1.03306	−0.516532	−	0.856268i	$-0.672777\pi$
$463$	−10292.0	−1.03306	−0.516532	+	0.856268i	$0.672777\pi$
$464$	−5076.48	−0.507909
$465$	58.2850	0.00581269
$466$	6291.05	0.625380
$467$	18023.0	1.78588	0.892938	−	0.450180i	$-0.148640\pi$
$467$	18023.0	1.78588	0.892938	+	0.450180i	$0.148640\pi$
$468$	3526.43	0.348310
$469$	8189.16	0.806269
$470$	−1939.67	−0.190362
$471$	−1339.74	−0.131066
$472$	12391.3	1.20838
$473$	0	0
$474$	223.941	0.0217003
$475$	6766.95	0.653661
$476$	3015.08	0.290328
$477$	10029.3	0.962704
$478$	−13053.0	−1.24902
$479$	17083.8	1.62960	0.814801	−	0.579741i	$-0.196846\pi$
$479$	17083.8	1.62960	0.814801	+	0.579741i	$0.196846\pi$
$480$	70.1121	0.00666701
$481$	−14422.9	−1.36721
$482$	10214.0	0.965221
$483$	−2699.42	−0.254302
$484$	0	0
$485$	−985.432	−0.0922601
$486$	−2847.10	−0.265735
$487$	461.804	0.0429699	0.0214850	−	0.999769i	$-0.493161\pi$
$487$	461.804	0.0429699	0.0214850	+	0.999769i	$0.493161\pi$
$488$	11466.3	1.06363
$489$	−998.391	−0.0923288
$490$	−1721.96	−0.158755
$491$	−12542.7	−1.15284	−0.576422	−	0.817152i	$-0.695552\pi$
$491$	−12542.7	−1.15284	−0.576422	+	0.817152i	$0.695552\pi$
$492$	198.323	0.0181730
$493$	6264.49	0.572289
$494$	−9308.48	−0.847790
$495$	0	0
$496$	−3176.41	−0.287550
$497$	11130.3	1.00455
$498$	400.551	0.0360424
$499$	−18277.0	−1.63966	−0.819829	−	0.572608i	$-0.805932\pi$
$499$	−18277.0	−1.63966	−0.819829	+	0.572608i	$0.805932\pi$
$500$	−733.395	−0.0655968
$501$	1418.67	0.126510
$502$	−4406.14	−0.391744
$503$	−2655.18	−0.235365	−0.117683	−	0.993051i	$-0.537547\pi$
$503$	−2655.18	−0.235365	−0.117683	+	0.993051i	$0.537547\pi$
$504$	−18460.7	−1.63156
$505$	−1701.11	−0.149898
$506$	0	0
$507$	−1334.57	−0.116904
$508$	1341.54	0.117168
$509$	−4887.16	−0.425579	−0.212789	−	0.977098i	$-0.568255\pi$
$509$	−4887.16	−0.425579	−0.212789	+	0.977098i	$0.568255\pi$
$510$	112.267	0.00974756
$511$	−8179.08	−0.708065
$512$	−12599.9	−1.08759
$513$	−1588.25	−0.136692
$514$	12732.0	1.09258
$515$	458.155	0.0392014
$516$	−215.148	−0.0183554
$517$	0	0
$518$	14663.8	1.24381
$519$	1130.42	0.0956064
$520$	2572.50	0.216945
$521$	−21941.1	−1.84502	−0.922512	−	0.385969i	$-0.873867\pi$
$521$	−21941.1	−1.84502	−0.922512	+	0.385969i	$0.873867\pi$
$522$	−7449.31	−0.624612
$523$	−6102.28	−0.510199	−0.255099	−	0.966915i	$-0.582108\pi$
$523$	−6102.28	−0.510199	−0.255099	+	0.966915i	$0.582108\pi$
$524$	−3211.77	−0.267761
$525$	−1856.59	−0.154340
$526$	−142.127	−0.0117814
$527$	3919.76	0.323999
$528$	0	0
$529$	19629.4	1.61333
$530$	1420.93	0.116455
$531$	13530.2	1.10577
$532$	−3005.45	−0.244930
$533$	13140.2	1.06785
$534$	1514.20	0.122708
$535$	918.660	0.0742377
$536$	7092.02	0.571508
$537$	−745.566	−0.0599135
$538$	−7461.44	−0.597929
$539$	0	0
$540$	85.2463	0.00679337
$541$	−2099.35	−0.166836	−0.0834179	−	0.996515i	$-0.526584\pi$
$541$	−2099.35	−0.166836	−0.0834179	+	0.996515i	$0.526584\pi$
$542$	−3666.18	−0.290546
$543$	−1983.58	−0.156765
$544$	4715.15	0.371619
$545$	2350.16	0.184716
$546$	2553.89	0.200177
$547$	−9029.06	−0.705767	−0.352884	−	0.935667i	$-0.614799\pi$
$547$	−9029.06	−0.705767	−0.352884	+	0.935667i	$0.614799\pi$
$548$	3095.68	0.241316
$549$	12520.2	0.973315
$550$	0	0
$551$	−6244.47	−0.482801
$552$	−2337.76	−0.180257
$553$	4790.62	0.368386
$554$	18383.3	1.40981
$555$	−173.394	−0.0132616
$556$	2061.83	0.157268
$557$	7894.54	0.600543	0.300271	−	0.953854i	$-0.402923\pi$
$557$	7894.54	0.600543	0.300271	+	0.953854i	$0.402923\pi$
$558$	−4661.12	−0.353621
$559$	−14254.9	−1.07857
$560$	−1946.19	−0.146860
$561$	0	0
$562$	2218.07	0.166484
$563$	−22377.6	−1.67514	−0.837569	−	0.546332i	$-0.816024\pi$
$563$	−22377.6	−1.67514	−0.837569	+	0.546332i	$0.816024\pi$
$564$	529.593	0.0395388
$565$	231.936	0.0172702
$566$	15984.4	1.18706
$567$	−19938.5	−1.47679
$568$	9639.11	0.712056
$569$	16920.5	1.24665	0.623325	−	0.781963i	$-0.285781\pi$
$569$	16920.5	1.24665	0.623325	+	0.781963i	$0.285781\pi$
$570$	−111.908	−0.00822335
$571$	−16320.0	−1.19609	−0.598047	−	0.801461i	$-0.704056\pi$
$571$	−16320.0	−1.19609	−0.598047	+	0.801461i	$0.704056\pi$
$572$	0	0
$573$	1893.35	0.138038
$574$	−13359.7	−0.971467
$575$	21868.8	1.58607
$576$	−15192.9	−1.09902
$577$	830.262	0.0599034	0.0299517	−	0.999551i	$-0.490465\pi$
$577$	830.262	0.0599034	0.0299517	+	0.999551i	$0.490465\pi$
$578$	−4556.01	−0.327863
$579$	−1396.37	−0.100226
$580$	335.161	0.0239945
$581$	8568.70	0.611858
$582$	−847.238	−0.0603422
$583$	0	0
$584$	−7083.29	−0.501899
$585$	2808.96	0.198523
$586$	15103.4	1.06470
$587$	21919.4	1.54124	0.770621	−	0.637294i	$-0.219946\pi$
$587$	21919.4	1.54124	0.770621	+	0.637294i	$0.219946\pi$
$588$	470.150	0.0329739
$589$	−3907.23	−0.273336
$590$	1916.93	0.133761
$591$	385.419	0.0268258
$592$	9449.63	0.656043
$593$	8236.51	0.570376	0.285188	−	0.958472i	$-0.407944\pi$
$593$	8236.51	0.570376	0.285188	+	0.958472i	$0.407944\pi$
$594$	0	0
$595$	2401.64	0.165475
$596$	684.843	0.0470676
$597$	−554.737	−0.0380299
$598$	−30082.2	−2.05711
$599$	−10922.0	−0.745009	−0.372505	−	0.928030i	$-0.621501\pi$
$599$	−10922.0	−0.745009	−0.372505	+	0.928030i	$0.621501\pi$
$600$	−1607.86	−0.109401
$601$	1386.44	0.0940997	0.0470498	−	0.998893i	$-0.485018\pi$
$601$	1386.44	0.0940997	0.0470498	+	0.998893i	$0.485018\pi$
$602$	14493.0	0.981216
$603$	7743.91	0.522979
$604$	−3624.16	−0.244147
$605$	0	0
$606$	−1462.55	−0.0980399
$607$	−1417.78	−0.0948035	−0.0474017	−	0.998876i	$-0.515094\pi$
$607$	−1417.78	−0.0948035	−0.0474017	+	0.998876i	$0.515094\pi$
$608$	−4700.08	−0.313509
$609$	1713.24	0.113997
$610$	1773.84	0.117739
$611$	35088.9	2.32331
$612$	2851.15	0.188318
$613$	15424.9	1.01632	0.508162	−	0.861261i	$-0.330325\pi$
$613$	15424.9	1.01632	0.508162	+	0.861261i	$0.330325\pi$
$614$	13251.1	0.870965
$615$	157.973	0.0103579
$616$	0	0
$617$	15169.5	0.989793	0.494897	−	0.868952i	$-0.335206\pi$
$617$	15169.5	0.989793	0.494897	+	0.868952i	$0.335206\pi$
$618$	393.904	0.0256394
$619$	−2081.56	−0.135162	−0.0675809	−	0.997714i	$-0.521528\pi$
$619$	−2081.56	−0.135162	−0.0675809	+	0.997714i	$0.521528\pi$
$620$	209.714	0.0135844
$621$	−5132.74	−0.331674
$622$	−14948.3	−0.963618
$623$	32392.3	2.08310
$624$	1645.77	0.105583
$625$	14745.9	0.943741
$626$	7986.59	0.509918
$627$	0	0
$628$	−4820.49	−0.306303
$629$	−11661.1	−0.739200
$630$	−2855.88	−0.180604
$631$	25249.7	1.59298	0.796492	−	0.604649i	$-0.206687\pi$
$631$	25249.7	1.59298	0.796492	+	0.604649i	$0.206687\pi$
$632$	4148.80	0.261124
$633$	−190.939	−0.0119892
$634$	16064.3	1.00630
$635$	1068.60	0.0667812
$636$	−387.959	−0.0241880
$637$	31150.5	1.93756
$638$	0	0
$639$	10525.1	0.651592
$640$	−1105.84	−0.0683005
$641$	−2626.57	−0.161846	−0.0809231	−	0.996720i	$-0.525787\pi$
$641$	−2626.57	−0.161846	−0.0809231	+	0.996720i	$0.525787\pi$
$642$	789.830	0.0485547
$643$	9229.61	0.566066	0.283033	−	0.959110i	$-0.408659\pi$
$643$	9229.61	0.566066	0.283033	+	0.959110i	$0.408659\pi$
$644$	−9712.70	−0.594308
$645$	−171.375	−0.0104618
$646$	−7525.99	−0.458369
$647$	316.901	0.0192561	0.00962803	−	0.999954i	$-0.496935\pi$
$647$	316.901	0.0192561	0.00962803	+	0.999954i	$0.496935\pi$
$648$	−17267.3	−1.04679
$649$	0	0
$650$	−20689.8	−1.24850
$651$	1071.99	0.0645389
$652$	−3592.29	−0.215774
$653$	−5022.66	−0.300998	−0.150499	−	0.988610i	$-0.548088\pi$
$653$	−5022.66	−0.300998	−0.150499	+	0.988610i	$0.548088\pi$
$654$	2020.58	0.120812
$655$	−2558.32	−0.152613
$656$	−8609.21	−0.512398
$657$	−7734.38	−0.459280
$658$	−35675.0	−2.11361
$659$	−24927.5	−1.47350	−0.736752	−	0.676163i	$-0.763642\pi$
$659$	−24927.5	−1.47350	−0.736752	+	0.676163i	$0.763642\pi$
$660$	0	0
$661$	−16440.5	−0.967418	−0.483709	−	0.875229i	$-0.660711\pi$
$661$	−16440.5	−0.967418	−0.483709	+	0.875229i	$0.660711\pi$
$662$	14487.8	0.850581
$663$	−2030.92	−0.118966
$664$	7420.72	0.433704
$665$	−2393.97	−0.139600
$666$	13866.6	0.806784
$667$	−20180.3	−1.17149
$668$	5104.47	0.295655
$669$	156.774	0.00906014
$670$	1097.14	0.0632630
$671$	0	0
$672$	1289.52	0.0740245
$673$	−11777.4	−0.674572	−0.337286	−	0.941402i	$-0.609509\pi$
$673$	−11777.4	−0.674572	−0.337286	+	0.941402i	$0.609509\pi$
$674$	3308.46	0.189076
$675$	−3530.17	−0.201298
$676$	−4801.87	−0.273206
$677$	−2818.49	−0.160005	−0.0800025	−	0.996795i	$-0.525493\pi$
$677$	−2818.49	−0.160005	−0.0800025	+	0.996795i	$0.525493\pi$
$678$	199.410	0.0112954
$679$	−18124.4	−1.02437
$680$	2079.89	0.117294
$681$	3003.19	0.168991
$682$	0	0
$683$	15803.2	0.885346	0.442673	−	0.896683i	$-0.354030\pi$
$683$	15803.2	0.885346	0.442673	+	0.896683i	$0.354030\pi$
$684$	−2842.04	−0.158871
$685$	2465.85	0.137540
$686$	−7795.34	−0.433860
$687$	3030.17	0.168280
$688$	9339.56	0.517540
$689$	−25704.8	−1.42130
$690$	−361.653	−0.0199535
$691$	3300.72	0.181716	0.0908578	−	0.995864i	$-0.471039\pi$
$691$	3300.72	0.181716	0.0908578	+	0.995864i	$0.471039\pi$
$692$	4067.32	0.223434
$693$	0	0
$694$	−13922.3	−0.761501
$695$	1642.34	0.0896365
$696$	1483.71	0.0808046
$697$	10624.0	0.577348
$698$	−3079.02	−0.166967
$699$	−1368.19	−0.0740340
$700$	−6680.16	−0.360695
$701$	−29773.2	−1.60416	−0.802082	−	0.597214i	$-0.796274\pi$
$701$	−29773.2	−1.60416	−0.802082	+	0.597214i	$0.796274\pi$
$702$	4856.04	0.261082
$703$	11623.8	0.623612
$704$	0	0
$705$	421.844	0.0225355
$706$	14745.8	0.786070
$707$	−31287.4	−1.66433
$708$	−523.385	−0.0277825
$709$	−24002.5	−1.27141	−0.635707	−	0.771931i	$-0.719291\pi$
$709$	−24002.5	−1.27141	−0.635707	+	0.771931i	$0.719291\pi$
$710$	1491.18	0.0788209
$711$	4530.15	0.238951
$712$	28052.5	1.47656
$713$	−12627.0	−0.663233
$714$	2064.84	0.108228
$715$	0	0
$716$	−2682.60	−0.140019
$717$	2838.80	0.147862
$718$	−5361.91	−0.278697
$719$	−20668.7	−1.07206	−0.536032	−	0.844198i	$-0.680077\pi$
$719$	−20668.7	−1.07206	−0.536032	+	0.844198i	$0.680077\pi$
$720$	−1840.38	−0.0952594
$721$	8426.52	0.435257
$722$	−9399.34	−0.484497
$723$	−2221.37	−0.114265
$724$	−7137.06	−0.366363
$725$	−13879.5	−0.710995
$726$	0	0
$727$	21928.9	1.11870	0.559351	−	0.828931i	$-0.311050\pi$
$727$	21928.9	1.11870	0.559351	+	0.828931i	$0.311050\pi$
$728$	47314.1	2.40876
$729$	−18438.0	−0.936745
$730$	−1095.79	−0.0555575
$731$	−11525.2	−0.583141
$732$	−484.315	−0.0244546
$733$	−25124.0	−1.26600	−0.633000	−	0.774152i	$-0.718177\pi$
$733$	−25124.0	−1.26600	−0.633000	+	0.774152i	$0.718177\pi$
$734$	−20857.1	−1.04884
$735$	374.495	0.0187938
$736$	−15189.3	−0.760712
$737$	0	0
$738$	−12633.3	−0.630133
$739$	37038.1	1.84367	0.921833	−	0.387588i	$-0.126692\pi$
$739$	37038.1	1.84367	0.921833	+	0.387588i	$0.126692\pi$
$740$	−623.887	−0.0309926
$741$	2024.43	0.100363
$742$	26134.1	1.29301
$743$	−24798.0	−1.22443	−0.612213	−	0.790693i	$-0.709721\pi$
$743$	−24798.0	−1.22443	−0.612213	+	0.790693i	$0.709721\pi$
$744$	928.375	0.0457471
$745$	545.508	0.0268267
$746$	−10469.8	−0.513843
$747$	8102.82	0.396876
$748$	0	0
$749$	16896.3	0.824268
$750$	−502.257	−0.0244531
$751$	13967.2	0.678654	0.339327	−	0.940668i	$-0.389801\pi$
$751$	13967.2	0.678654	0.339327	+	0.940668i	$0.389801\pi$
$752$	−22989.6	−1.11482
$753$	958.256	0.0463756
$754$	19092.4	0.922152
$755$	−2886.80	−0.139154
$756$	1567.88	0.0754274
$757$	−8515.45	−0.408850	−0.204425	−	0.978882i	$-0.565532\pi$
$757$	−8515.45	−0.408850	−0.204425	+	0.978882i	$0.565532\pi$
$758$	11958.1	0.573006
$759$	0	0
$760$	−2073.24	−0.0989530
$761$	−31658.0	−1.50802	−0.754009	−	0.656865i	$-0.771882\pi$
$761$	−31658.0	−1.50802	−0.754009	+	0.656865i	$0.771882\pi$
$762$	918.742	0.0436778
$763$	43224.9	2.05091
$764$	6812.40	0.322597
$765$	2271.07	0.107334
$766$	−20160.8	−0.950966
$767$	−34677.6	−1.63251
$768$	1487.57	0.0698932
$769$	−606.519	−0.0284416	−0.0142208	−	0.999899i	$-0.504527\pi$
$769$	−606.519	−0.0284416	−0.0142208	+	0.999899i	$0.504527\pi$
$770$	0	0
$771$	−2768.99	−0.129342
$772$	−5024.24	−0.234231
$773$	−4699.76	−0.218679	−0.109339	−	0.994004i	$-0.534874\pi$
$773$	−4699.76	−0.218679	−0.109339	+	0.994004i	$0.534874\pi$
$774$	13705.0	0.636457
$775$	−8684.55	−0.402527
$776$	−15696.2	−0.726107
$777$	−3189.12	−0.147245
$778$	3092.00	0.142485
$779$	−10590.0	−0.487068
$780$	−108.658	−0.00498791
$781$	0	0
$782$	−24321.8	−1.11221
$783$	3257.60	0.148681
$784$	−20409.2	−0.929720
$785$	−3839.73	−0.174581
$786$	−2199.55	−0.0998158
$787$	24078.1	1.09059	0.545293	−	0.838245i	$-0.316418\pi$
$787$	24078.1	1.09059	0.545293	+	0.838245i	$0.316418\pi$
$788$	1386.77	0.0626923
$789$	30.9101	0.00139472
$790$	641.821	0.0289050
$791$	4265.85	0.191752
$792$	0	0
$793$	−32088.9	−1.43696
$794$	−28384.8	−1.26869
$795$	−309.026	−0.0137862
$796$	−1995.99	−0.0888767
$797$	−18977.7	−0.843443	−0.421722	−	0.906725i	$-0.638574\pi$
$797$	−18977.7	−0.843443	−0.421722	+	0.906725i	$0.638574\pi$
$798$	−2058.25	−0.0913046
$799$	28369.7	1.25613
$800$	−10446.8	−0.461688
$801$	30631.1	1.35118
$802$	−3697.79	−0.162810
$803$	0	0
$804$	−299.554	−0.0131399
$805$	−7736.59	−0.338732
$806$	11946.3	0.522072
$807$	1622.73	0.0707842
$808$	−27095.7	−1.17973
$809$	9120.70	0.396374	0.198187	−	0.980164i	$-0.436495\pi$
$809$	9120.70	0.396374	0.198187	+	0.980164i	$0.436495\pi$
$810$	−2671.25	−0.115874
$811$	39874.2	1.72648	0.863239	−	0.504796i	$-0.168432\pi$
$811$	39874.2	1.72648	0.863239	+	0.504796i	$0.168432\pi$
$812$	6164.38	0.266413
$813$	797.329	0.0343955
$814$	0	0
$815$	−2861.41	−0.122983
$816$	1330.62	0.0570847
$817$	11488.4	0.491956
$818$	225.203	0.00962597
$819$	51663.2	2.20422
$820$	568.400	0.0242066
$821$	4913.94	0.208889	0.104444	−	0.994531i	$-0.466694\pi$
$821$	4913.94	0.208889	0.104444	+	0.994531i	$0.466694\pi$
$822$	2120.04	0.0899575
$823$	2777.58	0.117643	0.0588215	−	0.998269i	$-0.481266\pi$
$823$	2777.58	0.117643	0.0588215	+	0.998269i	$0.481266\pi$
$824$	7297.58	0.308523
$825$	0	0
$826$	35256.8	1.48516
$827$	20306.5	0.853842	0.426921	−	0.904289i	$-0.359598\pi$
$827$	20306.5	0.853842	0.426921	+	0.904289i	$0.359598\pi$
$828$	−9184.62	−0.385492
$829$	−35572.7	−1.49034	−0.745170	−	0.666875i	$-0.767632\pi$
$829$	−35572.7	−1.49034	−0.745170	+	0.666875i	$0.767632\pi$
$830$	1147.99	0.0480088
$831$	−3998.05	−0.166896
$832$	38938.9	1.62255
$833$	25185.4	1.04757
$834$	1412.02	0.0586262
$835$	4065.93	0.168512
$836$	0	0
$837$	2038.32	0.0841751
$838$	−4634.56	−0.191048
$839$	7096.72	0.292021	0.146011	−	0.989283i	$-0.453357\pi$
$839$	7096.72	0.292021	0.146011	+	0.989283i	$0.453357\pi$
$840$	568.817	0.0233644
$841$	−11581.2	−0.474851
$842$	−17938.2	−0.734195
$843$	−482.391	−0.0197087
$844$	−687.013	−0.0280189
$845$	−3824.90	−0.155717
$846$	−33735.3	−1.37097
$847$	0	0
$848$	16841.3	0.681995
$849$	−3476.33	−0.140527
$850$	−16727.9	−0.675015
$851$	37564.6	1.51316
$852$	−407.139	−0.0163713
$853$	24157.6	0.969682	0.484841	−	0.874602i	$-0.338877\pi$
$853$	24157.6	0.969682	0.484841	+	0.874602i	$0.338877\pi$
$854$	32624.9	1.30726
$855$	−2263.81	−0.0905504
$856$	14632.6	0.584267
$857$	28806.8	1.14822	0.574108	−	0.818779i	$-0.305349\pi$
$857$	28806.8	1.14822	0.574108	+	0.818779i	$0.305349\pi$
$858$	0	0
$859$	11244.4	0.446628	0.223314	−	0.974747i	$-0.428312\pi$
$859$	11244.4	0.446628	0.223314	+	0.974747i	$0.428312\pi$
$860$	−616.620	−0.0244495
$861$	2905.49	0.115005
$862$	16929.9	0.668949
$863$	−1291.92	−0.0509589	−0.0254794	−	0.999675i	$-0.508111\pi$
$863$	−1291.92	−0.0509589	−0.0254794	+	0.999675i	$0.508111\pi$
$864$	2451.93	0.0965468
$865$	3239.80	0.127349
$866$	2763.05	0.108421
$867$	990.851	0.0388132
$868$	3857.12	0.150829
$869$	0	0
$870$	229.531	0.00894464
$871$	−19847.4	−0.772105
$872$	37433.9	1.45375
$873$	−17138.9	−0.664450
$874$	24244.0	0.938291
$875$	−10744.4	−0.415118
$876$	299.186	0.0115394
$877$	26823.1	1.03278	0.516391	−	0.856353i	$-0.327275\pi$
$877$	26823.1	1.03278	0.516391	+	0.856353i	$0.327275\pi$
$878$	17531.9	0.673889
$879$	−3284.73	−0.126042
$880$	0	0
$881$	−28515.7	−1.09049	−0.545243	−	0.838278i	$-0.683563\pi$
$881$	−28515.7	−1.09049	−0.545243	+	0.838278i	$0.683563\pi$
$882$	−29948.8	−1.14334
$883$	41686.4	1.58874	0.794371	−	0.607433i	$-0.207801\pi$
$883$	41686.4	1.58874	0.794371	+	0.607433i	$0.207801\pi$
$884$	−7307.41	−0.278026
$885$	−416.899	−0.0158349
$886$	−34638.8	−1.31345
$887$	49179.3	1.86164	0.930822	−	0.365473i	$-0.119093\pi$
$887$	49179.3	1.86164	0.930822	+	0.365473i	$0.119093\pi$
$888$	−2761.86	−0.104372
$889$	19654.0	0.741478
$890$	4339.74	0.163448
$891$	0	0
$892$	564.085	0.0211737
$893$	−28279.0	−1.05971
$894$	469.007	0.0175458
$895$	−2136.81	−0.0798053
$896$	−20339.0	−0.758346
$897$	6542.35	0.243526
$898$	−37759.5	−1.40318
$899$	8014.01	0.297310
$900$	−6316.96	−0.233962
$901$	−20782.5	−0.768442
$902$	0	0
$903$	−3151.98	−0.116159
$904$	3694.33	0.135920
$905$	−5684.98	−0.208812
$906$	−2481.97	−0.0910130
$907$	52977.8	1.93947	0.969734	−	0.244163i	$-0.0785133\pi$
$907$	52977.8	1.93947	0.969734	+	0.244163i	$0.0785133\pi$
$908$	10805.7	0.394934
$909$	−29586.3	−1.07955
$910$	7319.52	0.266637
$911$	−31469.8	−1.14450	−0.572251	−	0.820078i	$-0.693930\pi$
$911$	−31469.8	−1.14450	−0.572251	+	0.820078i	$0.693930\pi$
$912$	−1326.37	−0.0481584
$913$	0	0
$914$	−17771.6	−0.643143
$915$	−385.778	−0.0139382
$916$	10902.8	0.393273
$917$	−47053.4	−1.69448
$918$	3926.15	0.141157
$919$	−42860.9	−1.53847	−0.769234	−	0.638967i	$-0.779362\pi$
$919$	−42860.9	−1.53847	−0.769234	+	0.638967i	$0.779362\pi$
$920$	−6700.09	−0.240104
$921$	−2881.89	−0.103107
$922$	−25034.4	−0.894211
$923$	−26975.6	−0.961984
$924$	0	0
$925$	25836.1	0.918361
$926$	−25360.5	−0.899996
$927$	7968.37	0.282325
$928$	9640.20	0.341008
$929$	−20968.3	−0.740525	−0.370262	−	0.928927i	$-0.620732\pi$
$929$	−20968.3	−0.740525	−0.370262	+	0.928927i	$0.620732\pi$
$930$	143.620	0.00506397
$931$	−25104.9	−0.883760
$932$	−4922.86	−0.173019
$933$	3250.98	0.114075
$934$	44410.4	1.55584
$935$	0	0
$936$	44741.6	1.56242
$937$	17126.8	0.597127	0.298563	−	0.954390i	$-0.403493\pi$
$937$	17126.8	0.597127	0.298563	+	0.954390i	$0.403493\pi$
$938$	20178.9	0.702415
$939$	−1736.94	−0.0603652
$940$	1517.83	0.0526660
$941$	−44021.2	−1.52503	−0.762513	−	0.646973i	$-0.776034\pi$
$941$	−44021.2	−1.52503	−0.762513	+	0.646973i	$0.776034\pi$
$942$	−3301.26	−0.114183
$943$	−34223.7	−1.18184
$944$	22720.1	0.783344
$945$	1248.88	0.0429906
$946$	0	0
$947$	8692.03	0.298261	0.149130	−	0.988818i	$-0.452353\pi$
$947$	8692.03	0.298261	0.149130	+	0.988818i	$0.452353\pi$
$948$	−175.238	−0.00600365
$949$	19823.0	0.678062
$950$	16674.5	0.569464
$951$	−3493.69	−0.119128
$952$	38253.9	1.30233
$953$	57906.0	1.96827	0.984133	−	0.177431i	$-0.0567787\pi$
$953$	57906.0	1.96827	0.984133	+	0.177431i	$0.0567787\pi$
$954$	24713.2	0.838699
$955$	5426.38	0.183867
$956$	10214.2	0.345556
$957$	0	0
$958$	42096.2	1.41969
$959$	45352.6	1.52713
$960$	468.129	0.0157383
$961$	−24776.6	−0.831679
$962$	−35539.5	−1.19110
$963$	15977.6	0.534654
$964$	−7992.67	−0.267040
$965$	−4002.03	−0.133503
$966$	−6651.64	−0.221545
$967$	−56564.3	−1.88106	−0.940530	−	0.339711i	$-0.889671\pi$
$967$	−56564.3	−1.88106	−0.940530	+	0.339711i	$0.889671\pi$
$968$	0	0
$969$	1636.77	0.0542628
$970$	−2428.20	−0.0803762
$971$	−30894.7	−1.02107	−0.510534	−	0.859857i	$-0.670552\pi$
$971$	−30894.7	−1.02107	−0.510534	+	0.859857i	$0.670552\pi$
$972$	2227.91	0.0735187
$973$	30206.3	0.995242
$974$	1137.93	0.0374350
$975$	4499.67	0.147800
$976$	21024.1	0.689513
$977$	−29998.9	−0.982342	−0.491171	−	0.871063i	$-0.663431\pi$
$977$	−29998.9	−0.982342	−0.491171	+	0.871063i	$0.663431\pi$
$978$	−2460.14	−0.0804361
$979$	0	0
$980$	1347.46	0.0439216
$981$	40874.8	1.33031
$982$	−30906.6	−1.00435
$983$	−24485.9	−0.794485	−0.397242	−	0.917714i	$-0.630033\pi$
$983$	−24485.9	−0.794485	−0.397242	+	0.917714i	$0.630033\pi$
$984$	2516.23	0.0815188
$985$	1104.62	0.0357321
$986$	15436.3	0.498573
$987$	7758.68	0.250214
$988$	7284.05	0.234551
$989$	37127.1	1.19370
$990$	0	0
$991$	−52661.1	−1.68803	−0.844014	−	0.536321i	$-0.819814\pi$
$991$	−52661.1	−1.68803	−0.844014	+	0.536321i	$0.819814\pi$
$992$	6031.98	0.193060
$993$	−3150.84	−0.100694
$994$	27426.1	0.875156
$995$	−1589.89	−0.0506562
$996$	−313.438	−0.00997155
$997$	−54748.6	−1.73912	−0.869561	−	0.493826i	$-0.835598\pi$
$997$	−54748.6	−1.73912	−0.869561	+	0.493826i	$0.835598\pi$
$998$	−45036.3	−1.42846
$999$	−6063.88	−0.192045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.a.b.1.2	✓	2
3.2	odd	2		1089.4.a.x.1.1		2
4.3	odd	2		1936.4.a.z.1.1		2
11.2	odd	10		121.4.c.d.81.2		8
11.3	even	5		121.4.c.g.9.2		8
11.4	even	5		121.4.c.g.27.2		8
11.5	even	5		121.4.c.g.3.1		8
11.6	odd	10		121.4.c.d.3.2		8
11.7	odd	10		121.4.c.d.27.1		8
11.8	odd	10		121.4.c.d.9.1		8
11.9	even	5		121.4.c.g.81.1		8
11.10	odd	2		121.4.a.e.1.1	yes	2
33.32	even	2		1089.4.a.k.1.2		2
44.43	even	2		1936.4.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.4.a.b.1.2	✓	2	1.1	even	1	trivial
121.4.a.e.1.1	yes	2	11.10	odd	2
121.4.c.d.3.2		8	11.6	odd	10
121.4.c.d.9.1		8	11.8	odd	10
121.4.c.d.27.1		8	11.7	odd	10
121.4.c.d.81.2		8	11.2	odd	10
121.4.c.g.3.1		8	11.5	even	5
121.4.c.g.9.2		8	11.3	even	5
121.4.c.g.27.2		8	11.4	even	5
121.4.c.g.81.1		8	11.9	even	5
1089.4.a.k.1.2		2	33.32	even	2
1089.4.a.x.1.1		2	3.2	odd	2
1936.4.a.y.1.1		2	44.43	even	2
1936.4.a.z.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} -1.32051 q^{6} -28.2487 q^{7} -24.4641 q^{8} -26.7128 q^{9} +O(q^{10})\)	\(q+2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} -1.32051 q^{6} -28.2487 q^{7} -24.4641 q^{8} -26.7128 q^{9} -3.78461 q^{10} +1.03332 q^{12} +68.4641 q^{13} -69.6077 q^{14} +0.823085 q^{15} -44.8564 q^{16} +55.3538 q^{17} -65.8231 q^{18} -55.1769 q^{19} +2.96152 q^{20} +15.1384 q^{21} -178.315 q^{23} +13.1103 q^{24} -122.641 q^{25} +168.703 q^{26} +28.7846 q^{27} +54.4693 q^{28} +113.172 q^{29} +2.02817 q^{30} +70.8128 q^{31} +85.1821 q^{32} +136.397 q^{34} +43.3872 q^{35} +51.5077 q^{36} -210.664 q^{37} -135.962 q^{38} -36.6898 q^{39} +37.5744 q^{40} +191.928 q^{41} +37.3027 q^{42} -208.210 q^{43} +41.0282 q^{45} -439.387 q^{46} +512.515 q^{47} +24.0385 q^{48} +454.990 q^{49} -302.200 q^{50} -29.6640 q^{51} -132.013 q^{52} -375.449 q^{53} +70.9282 q^{54} +691.079 q^{56} +29.5692 q^{57} +278.867 q^{58} -506.508 q^{59} -1.58708 q^{60} -468.697 q^{61} +174.490 q^{62} +754.603 q^{63} +568.749 q^{64} -105.154 q^{65} -289.895 q^{67} -106.733 q^{68} +95.5589 q^{69} +106.910 q^{70} -394.010 q^{71} +653.505 q^{72} +289.538 q^{73} -519.098 q^{74} +65.7231 q^{75} +106.392 q^{76} -90.4074 q^{78} -169.587 q^{79} +68.8949 q^{80} +705.820 q^{81} +472.931 q^{82} -303.331 q^{83} -29.1900 q^{84} -85.0179 q^{85} -513.051 q^{86} -60.6486 q^{87} -1146.68 q^{89} +101.098 q^{90} -1934.02 q^{91} +343.828 q^{92} -37.9485 q^{93} +1262.89 q^{94} +84.7461 q^{95} -45.6489 q^{96} +641.600 q^{97} +1121.14 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} + 2 q^{9} + 34 q^{10} - 88 q^{12} + 130 q^{13} - 160 q^{14} + 64 q^{15} - 62 q^{16} - 14 q^{17} - 194 q^{18} - 48 q^{19} - 98 q^{20} - 136 q^{21} - 128 q^{23} + 144 q^{24} - 176 q^{25} - 106 q^{26} + 16 q^{27} + 296 q^{28} - 30 q^{29} - 280 q^{30} - 184 q^{31} + 302 q^{32} + 446 q^{34} - 128 q^{35} + 394 q^{36} + 126 q^{37} - 168 q^{38} - 496 q^{39} + 186 q^{40} + 370 q^{41} + 712 q^{42} - 264 q^{43} - 202 q^{45} - 664 q^{46} + 256 q^{47} + 152 q^{48} + 522 q^{49} - 64 q^{50} + 488 q^{51} + 602 q^{52} - 162 q^{53} + 128 q^{54} + 336 q^{56} - 24 q^{57} + 918 q^{58} - 1304 q^{59} + 752 q^{60} - 300 q^{61} + 1312 q^{62} + 1336 q^{63} - 262 q^{64} - 626 q^{65} - 656 q^{67} - 934 q^{68} - 280 q^{69} + 872 q^{70} - 1176 q^{71} + 150 q^{72} - 668 q^{73} - 2022 q^{74} + 464 q^{75} + 192 q^{76} + 1960 q^{78} + 416 q^{79} + 214 q^{80} + 26 q^{81} - 322 q^{82} - 960 q^{83} - 1832 q^{84} + 502 q^{85} - 264 q^{86} + 1008 q^{87} - 1074 q^{89} + 1186 q^{90} - 688 q^{91} + 944 q^{92} + 1864 q^{93} + 2408 q^{94} + 24 q^{95} - 1664 q^{96} - 338 q^{97} + 822 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 + 2 * q^9 + 34 * q^10 - 88 * q^12 + 130 * q^13 - 160 * q^14 + 64 * q^15 - 62 * q^16 - 14 * q^17 - 194 * q^18 - 48 * q^19 - 98 * q^20 - 136 * q^21 - 128 * q^23 + 144 * q^24 - 176 * q^25 - 106 * q^26 + 16 * q^27 + 296 * q^28 - 30 * q^29 - 280 * q^30 - 184 * q^31 + 302 * q^32 + 446 * q^34 - 128 * q^35 + 394 * q^36 + 126 * q^37 - 168 * q^38 - 496 * q^39 + 186 * q^40 + 370 * q^41 + 712 * q^42 - 264 * q^43 - 202 * q^45 - 664 * q^46 + 256 * q^47 + 152 * q^48 + 522 * q^49 - 64 * q^50 + 488 * q^51 + 602 * q^52 - 162 * q^53 + 128 * q^54 + 336 * q^56 - 24 * q^57 + 918 * q^58 - 1304 * q^59 + 752 * q^60 - 300 * q^61 + 1312 * q^62 + 1336 * q^63 - 262 * q^64 - 626 * q^65 - 656 * q^67 - 934 * q^68 - 280 * q^69 + 872 * q^70 - 1176 * q^71 + 150 * q^72 - 668 * q^73 - 2022 * q^74 + 464 * q^75 + 192 * q^76 + 1960 * q^78 + 416 * q^79 + 214 * q^80 + 26 * q^81 - 322 * q^82 - 960 * q^83 - 1832 * q^84 + 502 * q^85 - 264 * q^86 + 1008 * q^87 - 1074 * q^89 + 1186 * q^90 - 688 * q^91 + 944 * q^92 + 1864 * q^93 + 2408 * q^94 + 24 * q^95 - 1664 * q^96 - 338 * q^97 + 822 * q^98

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